Detector flying-around asteroid attitude tracking control method based on adaptive iterative learning

Abstract

The invention belongs to the technical field of detector attitude tracking control, and particularly relates to a detector flying-around asteroid attitude tracking control method based on adaptive iterative learning, which comprises the following steps: step 1, outputting two state variables, namely attitude and angular velocity, by a detector mathematical model; 2, the attitude and the angular velocity are fed back to the input end of a control system, the attitude and the angular velocity are subtracted from a given expected attitude and a given expected angular velocity respectively, and an error attitude and an error angular velocity are obtained; 3, establishing a detector attitude tracking error system according to the two error states, regarding uncertainty and external interference in the system as total disturbance, and estimating the total disturbance through an adaptive law; and 4, designing an attitude tracking controller based on a self-adaptive iterative learning algorithm. The invention provides a self-adaptive iterative learning controller design method based on an all-drive system method and sliding mode control. The designed adaptive iterative learning controller has the characteristics of excellent control performance and less adjustment parameters.

Description

Technical Field

[0001] The present invention belongs to the technical field of probe attitude tracking control, and in particular relates to a probe attitude tracking control method for flying around an asteroid based on adaptive iterative learning. Background Art

[0002] When the probe flies around an asteroid for observation, attitude control is required to ensure that the payload on the probe can stably point to the surface of the asteroid. Due to the uncertainty of the gravitational field of an irregular asteroid, the probe needs to have strong anti-interference capabilities during the process of flying around the asteroid due to the uncertainty of the gravitational field and the influence of various complex perturbations such as solar gravity and light pressure. At the same time, the irregular shape and gravitational field distribution of the asteroid make the dynamic environment near it very complex, so the precise control capability of the probe is extremely high, otherwise it may escape.

[0003] Iterative learning control can significantly suppress repeated disturbances during periodic operation and achieve high-precision control; the motion process of a probe flying around an asteroid and carrying out observation missions has the characteristics of repeated operation, so the research on iterative learning attitude tracking control is of great value. As the complexity of tasks increases, how to design more technically advanced adaptive iterative control methods based on the characteristics of different systems still needs to be explored in depth. To this end, the present invention proposes an attitude tracking control method for a probe flying around an asteroid based on adaptive iterative learning. Summary of the invention

[0004] The purpose of the present invention is to provide a probe attitude tracking control method for flying around an asteroid based on adaptive iterative learning, so as to improve the robustness and adaptability of the attitude control system when the probe flies around an asteroid for observation. Probe attitude tracking control method based on adaptive iterative learning. First, based on the kinematic and dynamic equations of the probe, a mathematical model of the probe attitude tracking error system is established. Taking into account factors such as the uncertainty of the probe's moment of inertia parameters and the repetitive interference torque it is subjected to, the attitude tracking error system model is converted into a general nonlinear system model. The total disturbance term in the adaptive law estimation model is constructed, and combined with the full drive system method and the sliding mode control technology, an adaptive iterative learning attitude tracking control method is designed to ultimately achieve the purpose of high-precision flying around an asteroid.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A probe attitude tracking control method for flying around an asteroid based on adaptive iterative learning comprises the following steps:

[0007] Step 1: First, the detector mathematical model outputs two state variables, namely attitude σ and angular velocity Ω;

[0008] Step 2: Feed the attitude σ and angular velocity Ω back to the input of the control system and compare them with the given desired attitude σ d and the desired angular velocity Ω d Subtract and get the error posture σ e and error angular velocity Ω e ;

[0009] Step 3: Establish the detector attitude tracking error system based on the two error states. The uncertainty and external interference in the system are regarded as the total disturbance. to estimate;

[0010] Step 4: Design a posture tracking controller u based on an adaptive iterative learning algorithm.

[0011] Preferably, in step 1, a mathematical model of the attitude control system of the probe when it flies around the asteroid is first established, and the attitude kinematic equation of the probe is expressed as:

[0012]

[0013] Where: is the modified Rodriguez parameter, represents the angular velocity of the detector, W(σ) is calculated by the following formula:

[0014] W(σ)=(1-σ T σ)I3+2σ × +2σσ T (2)

[0015] The attitude dynamics equation of the probe is expressed as

[0016]

[0017] Where: represents the moment of inertia of the detector, is the control torque vector acting on the three main axes of the detector, represents the combined torque of solar light pressure and solar gravitational disturbance on the detector, Ω × is a skew-symmetric matrix, defined as:

[0018]

[0019] Due to the uncertainty of internal parameters caused by factors such as the rotation of the detector's own load and fuel consumption during operation, the moment of inertia J is expressed as:

[0020] J=J0+ΔJ (4)

[0021] Where: J0 is a known symmetric positive definite matrix, ΔJ represents the uncertain part of the moment of inertia J; In addition, in the probe attitude dynamics equation (3), It represents the component of the gravitational torque on the detector in the fixed coordinate system, which is calculated as:

[0022]

[0023]

[0024] Where: c mn is the mnth term in the rotation matrix C, where m is the asteroid gravity coefficient, R c represents the distance from the probe mass center to the asteroid mass center, and defines the system parameter variables a and b as

[0025]

[0026] Where: R0 is the reference radius of the asteroid, C 20 and C 22 is the spherical harmonic coefficient, I is the longitude of the detector, satisfying η represents the true anomaly angle, and ω0 represents the angular velocity of rotation.

[0027] Preferably, in step 2, when the probe flies around the asteroid for observation, σ d and Ω d represents the target attitude and target angular velocity, and the relationship between the two is

[0028]

[0029] The actual pose of the detector σ and the target pose σ d The error between e Calculated by the following formula

[0030]

[0031] The error angular velocity is defined as

[0032] ω=Ω-CΩ d (7)

[0033] Where: C represents the rotation matrix, which can be calculated by the following formula

[0034]

[0035] Where I3 represents a 3×3 unit matrix. Based on (6) and (7), the attitude kinematics equation (1) and the attitude dynamics equation (3), the following detector attitude tracking error system model is established:

[0036]

[0037] Where: represents the moment of inertia of the detector, is the control torque vector acting on the three main axes of the detector, It represents the combined torque of solar light pressure and solar gravitational disturbance on the detector;

[0038] Defining state variables Then the detector attitude tracking control error system model (8)-(9) is transformed into

[0039]

[0040] Where:

[0041]

[0042] in,

[0043]

[0044] Preferably, in step 3, in order to construct an adaptive iterative learning controller, it is assumed that the total disturbance term of the detector attitude tracking error system (10) has an upper bound, that is,

[0045] ||z||≤D (11)Where: D is a time-varying and unknown parameter;

[0046] In order to utilize the all-wheel drive system approach, the sliding surface is designed as follows:

[0047] s k =Kx k +a∫σ ek (12)

[0048] Where: K is a constant matrix that needs to be properly designed to ensure that the matrix KG is reversible, a>0 is the controller parameter; k∈Z + Represents the number of iterations, meaning: s k , x k and σ ek Respectively represent the sliding surface, state variable and posture tracking error corresponding to the kth iteration; taking the derivative of the sliding surface, we can get

[0049]

[0050] At this time, let the total disturbance z in the above formula be k is zero, the equivalent control term of sliding mode control designed by the full drive system method is

[0051]

[0052] z kFor the total disturbance, a differential adaptive law of the following form is designed to estimate the upper bound D of the total disturbance term:

[0053]

[0054] Where: γ is a constant, representing the adaptive factor, Represents the estimated value of the upper bound D.

[0055] Preferably, in step 4, the estimated value of the adaptive law (15) is used to design the switching control term of the sliding mode controller as:

[0056]

[0057] Where: η is a positive number; Based on the above results, the adaptive iterative learning posture tracking controller is designed as

[0058]

[0059] In the formula and See (14) and (16) for the definition of

[0060] The technical effects achieved by the present invention are:

[0061] In the present invention, a design method of an adaptive iterative learning controller based on an all-wheel drive system method and sliding mode control is proposed; the designed adaptive iterative learning controller has the characteristics of excellent control performance and fewer adjustment parameters.

[0062] In the present invention, for a probe flying around an asteroid, the present invention considers both the uncertainty of the moment of inertia parameters and the influence of external disturbances, and designs a new attitude tracking control method based on adaptive iterative learning technology. The method has the advantages of high tracking accuracy and few adjustment parameters. A simulation example illustrates the effectiveness of the proposed probe attitude tracking control method.

[0063] The purpose of the present invention is to improve the robustness and adaptability of the attitude control system when the probe flies around an asteroid for observation. A probe attitude tracking control method based on adaptive iterative learning. First, based on the kinematic and dynamic equations of the probe, a mathematical model of the probe attitude tracking error system is established. Taking into account factors such as the uncertainty of the probe's moment of inertia parameters and the repetitive interference torque it is subjected to, the attitude tracking error system model is converted into a general nonlinear system model. The total disturbance term in the adaptive law estimation model is constructed, and an adaptive iterative learning attitude tracking control method is designed in combination with the full drive system method and the sliding mode control technology, ultimately achieving the purpose of high-precision flying around an asteroid. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1It is a flowchart of a method for attitude tracking control of a probe flying around an asteroid based on adaptive iterative learning in the present invention;

[0065] Figure 2 is the attitude error variation curve under the action of the controller in the present invention;

[0066] Figure 3 is the error angular velocity variation curve under the action of the controller in the present invention;

[0067] Figure 4 It is a curve showing the variation of the performance index along the iteration axis in the present invention. DETAILED DESCRIPTION

[0068] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is specifically described below in conjunction with embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present invention, and does not strictly limit the scope of protection of the specific claims of the present invention.

[0069] A probe attitude tracking control method for flying around an asteroid based on adaptive iterative learning comprises the following steps:

[0070] Step 1: First, the detector mathematical model outputs two state variables, namely attitude σ and angular velocity Ω;

[0071] Step 2: Feed the attitude σ and angular velocity Ω back to the input of the control system and compare them with the given desired attitude σ d and the desired angular velocity Ω d Subtract and get the error posture σ e and error angular velocity Ω e ;

[0072] Step 3: Establish the detector attitude tracking error system based on the two error states. The uncertainty and external interference in the system are regarded as the total disturbance. to estimate;

[0073] Step 4: Design a posture tracking controller u based on an adaptive iterative learning algorithm.

[0074] In step 1, a mathematical model of the attitude control system of the probe when it flies around the asteroid is first established, and the attitude kinematic equation of the probe is expressed as:

[0075]

[0076] Where: is the modified Rodriguez parameter, represents the angular velocity of the detector, W(σ) is calculated by the following formula:

[0077] W(σ)=(1-σT σ)I3+2σ × +2σσ T (2)

[0078] Where I3 represents a 3×3 unit matrix; the attitude dynamics equation of the detector is expressed as

[0079]

[0080] Where: represents the moment of inertia of the detector, is the control torque vector acting on the three main axes of the detector, It represents the combined torque of solar light pressure and solar gravitational disturbance on the probe. This disturbance torque may appear repeatedly during the probe's flyby. × is a skew-symmetric matrix, defined as:

[0081]

[0082] Due to the uncertainty of internal parameters caused by factors such as the rotation of the detector's own load and fuel consumption during operation, the moment of inertia J is expressed as:

[0083] J=J0+ΔJ (4)

[0084] Where: J0 is a known symmetric positive definite matrix, ΔJ represents the uncertain part of the moment of inertia J; In addition, in the probe attitude dynamics equation (3), It represents the component of the gravitational torque on the detector in the fixed coordinate system, which is calculated as:

[0085]

[0086] Where: c mn is the mnth term in the rotation matrix C, where m is the asteroid gravity coefficient, R c represents the distance from the probe mass center to the asteroid mass center, and defines the system parameter variables a and b as

[0087]

[0088] Where: R0 is the reference radius of the asteroid, C 20 and C 22 is the spherical harmonic coefficient, I is the longitude of the detector, satisfying η represents the true anomaly angle, and ω0 represents the angular velocity of rotation.

[0089] In step 2, when the probe flies around the asteroid for observation, it is required that the probe can accurately track the target attitude; the present invention uses σ d and Ω drepresents the target attitude and target angular velocity, and the relationship between the two is

[0090]

[0091] The actual pose of the detector σ and the target pose σ d The error between e Calculated by the following formula

[0092]

[0093] The error angular velocity is defined as

[0094] ω=Ω-CΩ d (7)

[0095] Where: C represents the rotation matrix, which can be calculated by the following formula

[0096]

[0097] Where I3 represents a 3×3 identity matrix. Based on (6) and (7), the attitude kinematics equation (1) and the attitude dynamics equation (3), the following detector attitude tracking error system model is established:

[0098]

[0099] Defining state variables Then the detector attitude tracking control error system model (8)-(9) is transformed into

[0100]

[0101] Where:

[0102]

[0103] in,

[0104]

[0105] Since the attitude control of the probe flying around the asteroid has the characteristics of repeated operation, the adaptive iterative learning method will be used in the next section to design the attitude tracking control strategy of the probe flying around the asteroid; that is, the core goal of the present invention is to design a controller u so that the attitude tracking error system (10) of the asteroid probe flying stage is asymptotically stable.

[0106] In step 3, in order to construct an adaptive iterative learning controller, it is assumed that the total disturbance term of the detector attitude tracking error system (10) has an upper bound, that is,

[0107] ||z||≤D (11)Where: D is a time-varying and unknown parameter;

[0108] In order to utilize the all-wheel drive system approach, the sliding surface is designed as follows:

[0109] s k =Kx k +a∫σ ek (12)

[0110] Where: K is a constant matrix that needs to be properly designed to ensure that the matrix KG is reversible, a>0 is the controller parameter, k∈Z + represents the number of iterations; taking the derivative of the sliding surface, we can get

[0111]

[0112] At this time, let the total disturbance z in the above formula be k is zero, the equivalent control term of sliding mode control designed by the full drive system method is

[0113]

[0114] In practical applications, the total disturbance z k The value of is difficult to obtain; therefore, the present invention designs a differential adaptive law of the following form to estimate the upper bound D of the total disturbance term:

[0115]

[0116] Where: γ is a constant, representing the adaptive factor, Represents the estimated value of the upper bound D.

[0117] In step 4, the estimated value of the adaptive law (15) is used to design the switching control term of the sliding mode controller as:

[0118]

[0119] Where: η is a positive number; Based on the above results, the adaptive iterative learning posture tracking controller is designed as

[0120]

[0121] In the formula and See (14) and (16) for the definition of .

[0122] The present invention is verified in the simulation experiment.

[0123] The designed control method is applied to the attitude control of the probe during the stage of flying around an asteroid to verify its effectiveness and superiority. In the invention, we considered the scenario of the NEAR probe orbiting the asteroid Eros433. When the probe orbits the asteroid to observe it, high-precision attitude pointing control is required. The parameters of the asteroid Eros433 are shown in Table 1.

[0124] Table 1: Parameters of asteroid Eros433

[0125]

[0126] The moment of inertia of the detector is

[0127]

[0128] The uncertain part of the moment of inertia is set to ΔJ = 0.1J0. Assume that the combined disturbance torque on the detector is:

[0129]

[0130] The initial attitude and attitude angular velocity of the detector are:

[0131] σ(0)=[0.553-0.894-0.988] T

[0132] and

[0133] Ω(0)=

[000] T rad / s

[0134] The desired posture is:

[0135] σ d =0.01[cos(0.2t)sin(0.2t)sin(0.1t)] T

[0136] Using the above formula, the desired angular velocity can be obtained by formula (5); in addition, the controller (17) parameters are set to γ ​​= 0.01, η = 5, a = 0.3, K = 0.4 [I3 I3].

[0137] First, the simulation comparison results of the 1st iteration and the 10th iteration under the action of the controller (17) are given. Figure 2 The following are the curves of the attitude tracking error changing with time at the 1st iteration and the 10th iteration. Figure 3 The curves showing the variation of the error angular velocity with time at the 1st iteration and the 10th iteration are given.

[0138] pass Figure 2 as well as Figure 3It can be seen that even if there are factors such as uncertainty in the moment of inertia parameters, external disturbances, and gravitational torques of other celestial bodies, the controller (17) can still make the state of the detector attitude tracking error system converge to zero. Moreover, Figure 2 as well as Figure 3 The results show that as the number of iterations increases, the overshoot of the attitude tracking error curve and the error angular velocity curve decreases, and the required adjustment time also decreases. In other words, the performance of the attitude tracking control system is effectively improved through multiple iterative learning of the controller.

[0139] In order to further illustrate the role of the adaptive iterative learning controller, the following performance indicators are defined:

[0140] max t∈[0,T] ||ω k (t)||(deg / s) (52)

[0141] Index (52) represents the maximum value of the error angular velocity during each iteration. Figure 4 The curve of performance index changing with the number of iterations is given.

[0142] Figure 4 The simulation curve in shows that with the increase of the number of iterations, the value of index (52) decreases monotonically. Each iterative learning further reduces the maximum value of the error angular velocity. The above simulation results prove the convergence of the proposed algorithm.

[0143] In the present invention, a design method of an adaptive iterative learning controller based on an all-wheel drive system method and sliding mode control is proposed; the designed adaptive iterative learning controller has the characteristics of excellent control performance and fewer adjustment parameters.

[0144] In the present invention, for a probe flying around an asteroid, the present invention considers both the uncertainty of the moment of inertia parameters and the influence of external disturbances, and designs a new attitude tracking control method based on adaptive iterative learning technology. The method has the advantages of high tracking accuracy and few adjustment parameters. A simulation example illustrates the effectiveness of the proposed probe attitude tracking control method.

[0145] The purpose of the present invention is to improve the robustness and adaptability of the attitude control system when the probe flies around an asteroid for observation. A probe attitude tracking control method based on adaptive iterative learning. First, based on the kinematic and dynamic equations of the probe, a mathematical model of the probe attitude tracking error system is established. Taking into account factors such as the uncertainty of the probe's moment of inertia parameters and the repetitive interference torque it is subjected to, the attitude tracking error system model is converted into a general nonlinear system model. The total disturbance term in the adaptive law estimation model is constructed, and an adaptive iterative learning attitude tracking control method is designed in combination with the full drive system method and the sliding mode control technology, ultimately achieving the purpose of high-precision flying around an asteroid.

[0146] The above is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. The structures, devices and operating methods not specifically described and explained in the present invention shall be implemented according to the conventional means in the art unless otherwise specified and limited.

Claims

1. A probe attitude tracking control method for flying around an asteroid based on adaptive iterative learning, characterized in that: The following steps are involved: Step 1: First, the detector mathematical model outputs two state variables, namely attitude σ and angular velocity Ω; Step 2: Feed the attitude σ and angular velocity Ω back to the input of the control system and compare them with the given desired attitude σ d and the desired angular velocity Ω d Subtract and get the error posture σ e and error angular velocity Ω e ; Step 3: Establish the detector attitude tracking error system based on the two error states. The uncertainty and external interference in the system are regarded as the total disturbance. to estimate; Step 4: Design a posture tracking controller u based on an adaptive iterative learning algorithm.

2. The method for tracking the attitude of a probe flying around an asteroid based on adaptive iterative learning according to claim 1, characterized in that: In step 1, a mathematical model of the attitude control system of the probe when it flies around the asteroid is first established, and the attitude kinematic equation of the probe is expressed as: Where: is the modified Rodriguez parameter, represents the angular velocity of the detector, W(σ) is calculated by the following formula: W(σ)=(1-σ T σ)I3+2σ × +2ss T (2) The attitude dynamics equation of the probe is expressed as Where: represents the moment of inertia of the detector, is the control torque vector acting on the three main axes of the detector, represents the combined torque of solar light pressure and solar gravitational disturbance on the detector, Ω × is a skew-symmetric matrix, defined as: Due to the uncertainty of internal parameters caused by factors such as the rotation of the detector's own load and fuel consumption during operation, the moment of inertia J is expressed as: J=J0+ΔJ (4) Where: J0 is a known symmetric positive definite matrix, ΔJ represents the uncertain part of the moment of inertia J; In addition, in the probe attitude dynamics equation (3), It represents the component of the gravitational torque on the detector in the fixed coordinate system, which is calculated as: Where: c mn is the mnth term in the rotation matrix C, where m is the asteroid gravity coefficient, R c represents the distance from the probe mass center to the asteroid mass center, and defines the system parameter variables a and b as Where: R0 is the reference radius of the asteroid, C 20 and C 22 is the spherical harmonic coefficient, I is the longitude of the detector, satisfying η represents the true anomaly, and ω0 represents the angular velocity of rotation.

3. The method for tracking the attitude of a probe flying around an asteroid based on adaptive iterative learning according to claim 1, characterized in that: In step 2, when the probe flies around the asteroid for observation, σ d and Ω d represents the target attitude and target angular velocity, and the relationship between the two is The actual pose of the detector σ and the target pose σ d The error between e Calculated by the following formula The error angular velocity is defined as ω=Ω-CΩ d (7) Where: C represents the rotation matrix, which can be calculated by the following formula Where I3 represents a 3×3 unit matrix. Based on (6) and (7), the attitude kinematics equation (1) and the attitude dynamics equation (3), the following detector attitude tracking error system model is established: Where: represents the moment of inertia of the detector, is the control torque vector acting on the three main axes of the detector, It represents the combined torque of solar light pressure and solar gravitational disturbance on the detector; Defining state variables Then the detector attitude tracking control error system model (8)-(9) is transformed into Where: in, 4. The method for tracking the attitude of a probe flying around an asteroid based on adaptive iterative learning according to claim 1, characterized in that: In step 3, in order to construct an adaptive iterative learning controller, it is assumed that the total disturbance term of the detector attitude tracking error system (10) has an upper bound, that is, ||z||≤D (11) Where: D is a time-varying and unknown parameter; In order to utilize the all-wheel drive system approach, the sliding surface is designed as follows: s k =Kx k +a∫σ ek (12) Where: K is a constant matrix that needs to be properly designed to ensure that the matrix KG is reversible, a>0 is the controller parameter; k∈Z + Represents the number of iterations, meaning: s k , x k and σ ek Respectively represent the sliding surface, state variable and posture tracking error corresponding to the kth iteration; taking the derivative of the sliding surface, we can get At this time, let the total disturbance z in the above formula be k is zero, the equivalent control term of sliding mode control designed by the full drive system method is z k For the total disturbance, a differential adaptive law of the following form is designed to estimate the upper bound D of the total disturbance term: Where: γ is a constant, representing the adaptive factor, Represents the estimated value of the upper bound D.

5. The method for tracking the attitude of a probe flying around an asteroid based on adaptive iterative learning according to claim 1, characterized in that: In step 4, the estimated value of the adaptive law (15) is used to design the switching control term of the sliding mode controller as: Where: η is a positive number; Based on the above results, the adaptive iterative learning posture tracking controller is designed as In the formula and See (14) and (16) for the definition of .

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